Mixed-element volume completion from NURBS surfaces

Abstract

In this paper we present a methodology to create a volumetric representation from a 2-manifold without boundaries represented with untrimmed NURBS surfaces. A trivariate NURBS representation is difficult to construct from such a representation, especially when the input surface patches were created with only a boundary representation as the goal. These kinds of inputs arise in numerous existing geometric modeling scenarios such as models from CAD systems, subdivision surfaces, quadrilateral meshing and data-fitting. Our approach, nearly automatic and only requiring minimal user input, creates a hybrid representation using trivariate NURBS elements at the boundary and unstructured tetrahedral elements in the interior of the object. The original boundary representation of the input model is maintained in the final representation, allowing the volumetric representation to be used in both computer graphics simulations and isogeometric analysis applications. We demonstrate that the hybrid representation yields convergence under model refinement, and that it can be used efficiently in elastic body simulation.